The present invention relates to an image reconstruction method in an in vivo tomographic imaging system utilizing a nuclear magnetic resonance (NMR) phenomenon, and more particularly to an image reconstruction method in an NMR imaging system which uses time-varying gradient magnetic fields and is useful for the reduction in time necessary for various measurements and the acquisition of a tomographic (or cross-sectional) image with high quality.
Prior art examples of an NMR imaging system for acquiring a tomographic image at a high speed by use of time-varying gradient magnetic fields are disclosed by I. Shenberg et al, "Resolution and Noise Considerations in NMR Systems with Time-Varying Gradients", IEEE Transactions on Medical Imaging, Vol. MI-4, No. 3, pp. 144-152, 1985, I. Shenberg et al, "Inhomogeneity and Multiple Dimension Considerations in Magnetic Resonance Imaging with Time-Varying Gradients", IEEE Transactions on Medical Imaging, Vol. MI-4, Vol. 3, pp. 165-174, 1985, and C. B. Ahn et al, "High-Speed Spiral-Scan Echo Planar NMR Imaging-I", IEEE Transactions on Medical Imaging, Vol. MI-5 No. 1, pp. 2-7, 1986. However, in these prior art examples, the control or correction of the point spread function or signal-to-noise (S/N) ratio of a reconstructed image is not sufficiently taken into consideration though a method of controlling the point spread function is disclosed in connection with only very special cases. Further, it is possible to correct the inhomogeneity effect of a static magnetic field.
Approaches for reducing the effect or artifact of spin-spin relaxation called T.sub.2, chemical shift and/or static magnetic field inhomogeneity in NMR imaging systems are described in, for example, A. Macovski et al, "A Novel Fast-Scanning System", Proceedings of 5th Annual Meeting Magnetic Resonance in Medicine, Works in Progress, pp. 156-157, 1986 from which there are known a method in which scans retraced in the opposite direction in a frequency domain are added for the reduction of effect of T.sub.2 relaxation and a method in which 180.degree. RF pulses are used for the reduction of effect of T.sub.2 relaxation chemical shift, and/or static magnetic field inhomogeneity. However, the method of adding such redundant scans is accompanied with the degradation of the S/N ratio or the increase of data measurement time. On the other hand, the method of using the 180.degree. RF pulses cannot avoid the degradation of an image quality due to the imperfection of 180.degree. RF pulses. Further, in both the methods, though the effect of T.sub.2 relaxation, chemical shift and/or inhomogeneity can be corrected to a certain extent, it is not possible to measure separately the effect of relaxation, etc.
In NMR imaging systems, many methods are known in which time required for measurement is reduced by measuring an NMR signal under time-varying gradient magnetic fields. Generally, in these methods, time for measurement of an NMR signal for one spin excitation becomes long (though the total measurement time is reduced since the times of spin excitation can be decreased). Therefore, the effect of relaxation, chemical shift and/or static magnetic field inhomogeneity should be corrected, otherwise, the quality of a reconstruction image is seriously degraded.
Also, approaches for simultaneously visualizing the position and velocity of nucleus spins are disclosed by, for example, K. Shimizu et al, "Visualization of Moving Fluid: Quantitative Analysis of Blood Flow Velocity Using MR Imaging", Radiography, Vol. 159, No. 1, pp. 195-199, 1986, and S. Ljunggren, "A Simple Graphical Representation of Fourier-Based Imaging Methods", Journal of Magnetic Resonance, Vol. 54, pp. 338-343, 1983. Shimizu et al disclose a method in which a new coordinate corresponding to a direction of velocity is introduced and the velocity and the position are simultaneously imaged through a multi-dimensional Fourier transform in combination of the new coordinate and usual position coordinates. However, this method involves a problem that measurement time becomes long since an imaging in the velocity direction requires many times of measurement because of the use of the Fourier transform for imaging. Ljunggren discloses a method in which data of the multi-dimensional Fourier domain is effectively collected by means of time-varying gradient magnetic fields. In principle, this method permits high-speed measurement. But, Ljunggren does not disclose any concrete image reconstruction method.